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Question: The magnetic susceptibility of a paramagnetic substance at \( -{{173}^{0}}C \) is \( 1.5\times {{10}...

The magnetic susceptibility of a paramagnetic substance at −1730C-{{173}^{0}}C is 1.5×10−21.5\times {{10}^{-2}} then its value at −730C-{{73}^{0}}C will be.
A)7.5×10−1 B)7.5×10−2 C)7.5×10−3 D)7.5×10−4 \begin{aligned} & A)7.5\times {{10}^{-1}} \\\ & B)7.5\times {{10}^{-2}} \\\ & C)7.5\times {{10}^{-3}} \\\ & D)7.5\times {{10}^{-4}} \\\ \end{aligned}

Explanation

Solution

Hint: The magnetic susceptibility of a material is defined as the ratio of the magnetization produced in a material to the magnetic field intensity. For a paramagnetic material, the magnetic susceptibility decreases with increase in temperature according to the Curie’s law.

Complete step-by-step answer:
Let us first of all learn what is meant by magnetic susceptibility. Magnetic susceptibility is a measure of the extent to which a material will be magnetized when placed in a magnetic field. It can be given as the ratio of magnetization to the applied magnetizing field intensity.
Mathematically,
If χ\chi is the magnetic susceptibility of a paramagnetic substance and TT is the temperature of the substance, then for a paramagnetic material by Curie’s law, we have,
χα1T\chi \alpha \dfrac{1}{T}
So, by using this proportionality condition, we can write the condition further as
χ1χ2=T2T1\dfrac{{{\chi }_{1}}}{{{\chi }_{2}}}=\dfrac{{{T}_{2}}}{{{T}_{1}}}
Now let us substitute the value of the parameters mentioned in the question,
T1=−1730C ⇒T1=(−173+273)K ⇒T1=100K χ1=1.5×10−2 T2=−730C ⇒T1=(−73+273)K ⇒T1=200K \begin{aligned} & {{T}_{1}}=-{{173}^{0}}C \\\ & \Rightarrow {{T}_{1}}=(-173+273)K \\\ & \Rightarrow {{T}_{1}}=100K \\\ & {{\chi }_{1}}=1.5\times {{10}^{-2}} \\\ & {{T}_{2}}=-{{73}^{0}}C \\\ & \Rightarrow {{T}_{1}}=(-73+273)K \\\ & \Rightarrow {{T}_{1}}=200K \\\ \end{aligned}
Therefore, after substitution we will get,
1.5×10−2χ2=200100 ⇒χ2=7.5×10−3 \begin{aligned} & \dfrac{1.5\times {{10}^{-2}}}{{{\chi }_{2}}}=\dfrac{200}{100} \\\ & \Rightarrow {{\chi }_{2}}=7.5\times {{10}^{-3}} \\\ \end{aligned}
Therefore from the above calculations, it is found that the magnetic susceptibility of the paramagnetic substance at the given temperature is 7.5×10−37.5\times {{10}^{-3}} .
So, the answer to the question is option C)7.5×10−3C)7.5\times {{10}^{-3}} .

Additional Information:
The temperature which we have considered is known as the Curie temperature. It is the temperature at which a paramagnetic substance gets converted into a ferromagnetic substance.

Note: Students must be very careful in using the proportionality condition. They must be very cautious while substituting the values of the respective parameters because many times it happens that the substitution becomes alternate and hence resulting in an incorrect result.